Instrumental Variables

TLDR

Instrumental variables (IV) are used to correct for confounding, but their adoption in medical research remains limited due to unfamiliarity or perceived inapplicability. The paper aims to show that IV in a linear model is easy to understand and apply once a suitable instrument is identified. The authors explain that IV estimation is straightforward in linear models but becomes problematic when the instrument is weakly correlated with the exposure. The IV estimator is imprecise and biased when instruments are weak or assumptions are violated; strong instruments are advised, yet their correlation with exposure is limited under strong confounding, making IV less useful when confounding is strong and more suitable for moderate confounding.

Abstract

To correct for confounding, the method of instrumental variables (IV) has been proposed. Its use in medical literature is still rather limited because of unfamiliarity or inapplicability. By introducing the method in a nontechnical way, we show that IV in a linear model is quite easy to understand and easy to apply once an appropriate instrumental variable has been identified. We also point out some limitations of the IV estimator when the instrumental variable is only weakly correlated with the exposure. The IV estimator will be imprecise (large standard error), biased when sample size is small, and biased in large samples when one of the assumptions is only slightly violated. For these reasons, it is advised to use an IV that is strongly correlated with exposure. However, we further show that under the assumptions required for the validity of the method, this correlation between IV and exposure is limited. Its maximum is low when confounding is strong, such as in case of confounding by indication. Finally, we show that in a study in which strong confounding is to be expected and an IV has been used that is moderately or strongly related to exposure, it is likely that the assumptions of IV are violated, resulting in a biased effect estimate. We conclude that instrumental variables can be useful in case of moderate confounding but are less useful when strong confounding exists, because strong instruments cannot be found and assumptions will be easily violated.